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Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums by Casals, Marc; Dolan, Sam R.; Ottewill, Adrian C.; Wardell, Barry is a scholarly article available to read on EtoBox.

What is Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums about?

We present the first application of the Poisson-Wiseman-Anderson method of matched expansions, to compute the self-force acting on a point particle moving in a curved spacetime. The method uses two expansions for the Green function, valid in `quasilocal' and `distant past' regimes, which are matched within the normal neighbourhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime (dS_2 x S^2), on which scalar perturbations are governed by a radial equation with a P\"oschl-Teller potential. We combine (i) a very high order quasilocal expansion, and (ii) an expansion in quasinormal modes, to determine the Green function globally. We show it is singular everywhere on the null wavefront (even outside the normal neighbourhood), and apply asymptotic methods to determine its singular structure. We find the Green function undergoes a transition every time the null wavefront passes through a caustic: the singular part follows a repeating four-fold sequence $\delta(\sigma)$, $1/\pi \sigma$, $-\delta(\sigma)$, $-1/\pi \sigma$ etc., where $\sigma$ is Synge's world function. The matched expansion method provides new insight into the non-local propertie

Author

Casals, Marc; Dolan, Sam R.; Ottewill, Adrian C.; Wardell, Barry

Published

2009

Language

EN